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Theorem mulcomi 7962
Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)
Hypotheses
Ref Expression
axi.1  |-  A  e.  CC
axi.2  |-  B  e.  CC
Assertion
Ref Expression
mulcomi  |-  ( A  x.  B )  =  ( B  x.  A
)

Proof of Theorem mulcomi
StepHypRef Expression
1 axi.1 . 2  |-  A  e.  CC
2 axi.2 . 2  |-  B  e.  CC
3 mulcom 7939 . 2  |-  ( ( A  e.  CC  /\  B  e.  CC )  ->  ( A  x.  B
)  =  ( B  x.  A ) )
41, 2, 3mp2an 426 1  |-  ( A  x.  B )  =  ( B  x.  A
)
Colors of variables: wff set class
Syntax hints:    = wceq 1353    e. wcel 2148  (class class class)co 5874   CCcc 7808    x. cmul 7815
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 7911
This theorem is referenced by:  mulcomli  7963  8th4div3  9137  numma2c  9428  nummul2c  9432  9t11e99  9512  binom2i  10628  fac3  10711  tanval2ap  11720  pockthi  12355  sincosq4sgn  14220  2logb9irrALT  14362  2lgsoddprmlem2  14424  2lgsoddprmlem3d  14428
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